NumberTopic Summary
Knowledge Organiser: Bounds and Error Intervals
Part of Bounds & Error Intervals · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Bounds and Error Intervals within Bounds & Error Intervals for GCSE Mathematics. Revise Bounds & Error Intervals in Number for GCSE Mathematics with 14 exam-style questions and 5 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 7 of 7 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 7 of 7
Practice
14 questions
Recall
5 flashcards
Knowledge Organiser: Bounds and Error Intervals
Key Terms
- Lower bound (LB): Smallest value that rounds to the given value
- Upper bound (UB): Smallest value that would round UP to the next value
- Error interval: Range of possible values written as an inequality
- Degree of accuracy: The precision of a measurement (e.g. nearest 10, 1 d.p.)
- Half interval: Half the degree of accuracy — added/subtracted to find bounds
Must-Know Facts
- Error interval: LB ≤ x < UB (lower uses ≤; upper uses <)
- LB = value − half interval; UB = value + half interval
- Rounded to nearest 10 → half interval = 5
- Rounded to 1 d.p. → half interval = 0.05
- Maximum of A + B: UB(A) + UB(B)
- Maximum of A ÷ B: UB(A) ÷ LB(B) (bigger top, smaller bottom)
- Minimum of A ÷ B: LB(A) ÷ UB(B)
Bounds in Calculations
- Max A + B: UB(A) + UB(B)
- Min A + B: LB(A) + LB(B)
- Max A − B: UB(A) − LB(B)
- Min A − B: LB(A) − UB(B)
- Max A × B: UB(A) × UB(B)
- Max A ÷ B: UB(A) ÷ LB(B)
Key Formulas
- Lower bound = rounded value − ½ × degree of accuracy
- Upper bound = rounded value + ½ × degree of accuracy
- Error interval: LB ≤ x < UB
- Max sum = UB(A) + UB(B); Min sum = LB(A) + LB(B)
- Max difference = UB(A) − LB(B); Min difference = LB(A) − UB(B)
Common Mistakes
- Error interval notation: Use ≤ x < UB (upper bound is strict inequality) — not ≤ x ≤ UB
- Max difference: Subtract the LOWER bound of B from UPPER bound of A — not both upper bounds
- Half the accuracy: For a measurement to 1 decimal place, the accuracy is 0.1 so bounds are ±0.05, not ±0.1
- Max division: Divide by the LOWER bound of the denominator to maximise the result
- Significant figures vs decimal places: Check which is stated — they give different bound widths